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The volume of a right cone is 180 pi units ^(3). If its radius measures 6 units, find its height. Answer: units

The volume of a right cone is 180π 180 \pi units 3 ^{3} . If its radius measures 66 units, find its height.\newlineAnswer: units

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Full solution

Q. The volume of a right cone is 180π 180 \pi units 3 ^{3} . If its radius measures 66 units, find its height.\newlineAnswer: units
  1. Write Formula: Write down the formula for the volume of a right cone.\newlineThe formula for the volume of a right cone is V=13πr2hV = \frac{1}{3} \pi r^2 h, where VV is the volume, rr is the radius, and hh is the height.
  2. Substitute Values: Substitute the given values into the formula.\newlineWe know that V=180πV = 180 \pi and r=6r = 6. So, we substitute these values into the formula to get 180π=(13)×π×62×h180 \pi = (\frac{1}{3}) \times \pi \times 6^2 \times h.
  3. Simplify Equation: Simplify the equation.\newlineFirst, calculate 626^2, which is 3636. Then, the equation becomes 180π=(13)⋅π⋅36⋅h180 \pi = (\frac{1}{3}) \cdot \pi \cdot 36 \cdot h.
  4. Isolate Variable: Isolate the variable hh. To isolate hh, we divide both sides of the equation by (1/3)×π×36(1/3) \times \pi \times 36. This gives us h=180π(1/3)×π×36h = \frac{180 \pi}{(1/3) \times \pi \times 36}.
  5. Simplify Right Side: Simplify the right side of the equation.\newlineThe pi terms cancel out, and we are left with h=180(13)×36h = \frac{180}{(\frac{1}{3}) \times 36}. Simplifying further, we get h=18012.h = \frac{180}{12}.
  6. Calculate Value: Calculate the value of hh.\newlineDividing 180180 by 1212 gives us h=15h = 15.

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